TY - JOUR
ID - 11176
TI - Nonnilpotent subsets in the Suzuki groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Zarrin, Mohammad
AD - University of Kurdistan
Y1 - 2017
PY - 2017
VL - 6
IS - 2
SP - 7
EP - 15
KW - Nilpotentlizer
KW - Hypercenter of a group
KW - Clique number
KW - Graphs associated to groups
DO - 10.22108/ijgt.2017.11176
N2 - Let $G$ be a group and $\mathcal{N}$ be the class of all nilpotent groups. A subset $A$ of $G$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $A$, $\langle a, b\rangle \not\in \mathcal{N}$. If, for any other nonnilpotent subset $B$ in $G$, $|A|\geq |B|$, then $A$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $\omega(\mathcal{N}_G)$. In this paper, among other results, we obtain $\omega(\mathcal{N}_{Suz(q)})$ and $\omega(\mathcal{N}_{PGL(2,q)})$, where $Suz(q)$ is the Suzuki simple group over the field with $q$ elements and $PGL(2,q)$ is the projective general linear group of degree $2$ over the finite field with $q$ elements, respectively.
UR - https://ijgt.ui.ac.ir/article_11176.html
L1 - https://ijgt.ui.ac.ir/article_11176_3a4049d20a5e0a7916fa9b1738b69f83.pdf
ER -